Working Through the Nuclear Fission Simulation Answer Key
I spend a lot of time helping people who are stuck on the uranium-235 fission simulations you find in most online physics labs. The PhET one is the most common, but there are a few others from university coursepages that pop up. The answer key you end up needing usually revolves around predicting what happens when you introduce a neutron to a U-235 nucleus, tracking the chain reaction, and understanding why control rods matter. Here is how the simulation actually behaves under normal conditions. When a slow-moving neutron strikes a U-235 nucleus, the nucleus absorbs the neutron and becomes unstable U-236. It splits almost immediately into two smaller nuclei — typically barium-141 and krypton-92, though the exact pairing varies each run. Three to four new neutrons are released in the process, along with a significant amount of kinetic energy. That is the core event everything else builds on. The chain reaction part is where most students get tripped up. Those newly released neutrons go on to hit other U-235 nuclei. If enough of them do, you get exponential growth. If too many escape the material without hitting anything, the reaction dies out. The simulation models this through a simple criticality threshold. When the neutron population stays steady or grows, criticality is achieved. When it shrinks, subcritical. When it drops too fast, you are below critical.
Control rods work by absorbing free neutrons without undergoing fission themselves. Most simulations use cadmium or boron as the rod material. Inserting them further into the uranium assembly removes more neutrons from the reaction loop. Pulling them out does the opposite. The trick the simulation hides is that the relationship is not perfectly linear. A small movement near the bottom of the rod's range can make a bigger difference than the same movement near the top, depending on neutron flux distribution. I ran into a specific issue last year with a version of the simulation that a professor was using for a summer course. The question asked students to set the enrichment level to 3 percent and observe whether a chain reaction could sustain itself with no control rods present. Most students reported that the reaction fizzled out, which is correct for low-enriched uranium in an unmoderated, unreflected geometry. But one student kept getting a sustained reaction even at 3 percent. I downloaded the simulation file myself and checked the configuration. The default neutron reflector was enabled in that build, which was not mentioned in the question text. The reflector was bouncing escaping neutrons back into the assembly, artificially pushing the system toward criticality. I had the student disable the reflector in the settings panel and the results matched the expected answer. That discrepancy cost us about forty minutes of back-and-forth. The counterintuitive thing nobody emphasizes is that fission does not require fast neutrons. Fast neutrons actually have a lower probability of causing fission in U-235 because the capture cross-section drops sharply at higher energies. That is why most real reactors use a moderator — water, heavy water, or graphite — to slow the neutrons down to thermal energies where the fission probability is highest. The simulation makes this visible when you toggle the moderator setting, but students often skip that part because the question does not directly ask about it.
Another thing that catches people is the difference between U-235 and U-238 in the simulation. U-238 can still undergo fission, but only when hit by a fast neutron with enough energy. For slow neutrons, U-238 tends to absorb the neutron without fissioning, turning into U-239. The simulation shows this as a gray absorption event rather than a split. If your answer key includes questions about why natural uranium cannot sustain a chain reaction in a light-water reactor, this distinction is the answer. Natural uranium is only about 0.7 percent U-235. The rest is U-238, which soaks up neutrons and starves the reaction. When you are filling out the answer key, pay attention to the energy values. Each fission event releases roughly 200 MeV of energy. The simulation displays this in joules or electron-volts depending on the unit setting. If a question asks for the total energy from a chain reaction with ten sequential fission events, the quick calculation is ten times two hundred MeV, which equals two thousand MeV or about 3.2 times ten to the minus eleven joules. Students sometimes forget to convert between units and mark the answer wrong even though their logic is sound. The main limitation of these simulations is that they are deterministic in ways that real reactors are not. The simulation gives you clean, repeatable outcomes for the same inputs. Real nuclear physics involves statistical distributions. The number of neutrons released per fission is an average, not a fixed number. The exact fragment masses vary from event to event. The simulation smooths all of that out, which is fine for an introductory course but misleading if you take it as a complete picture. For a more realistic model, you would need something like MCNP or Geant4, but those are not designed for homework assignments.
Get the Full Details
If you are looking for the downloadable simulation file, the PhET version is freely available from the University of Colorado's site. Look for "Nuclear Fission" in their simulations library. The .jar or HTML5 version works in most browsers without installation. Some instructors host modified versions on their own servers, so check your course LMS first before searching elsewhere. The answer key itself is usually provided by the instructor or posted on the course page. There is no single universal answer key since different professors adjust the parameters and questions. A few practical notes for getting through the assignment faster. First, take screenshots of each configuration before you change anything. The simulation does not always reset cleanly, and you will not want to re-run five different enrichment levels from scratch. Second, write down the neutron count after each generation rather than relying on memory. Third, if the simulation lags during a chain reaction, reduce the time step or slow the animation speed. I have seen students miss the critical moment because the frame rate dropped during a fast cascade and they could not tell whether the reaction was stabilizing or accelerating. The questions that tend to trip people up are the ones asking about delayed neutrons. Only a small fraction of the neutrons from fission are emitted seconds or minutes after the split rather than instantly. These delayed neutrons are what make reactor control possible. Without them, the reaction would change too quickly for any mechanical system to respond. The basic simulation may not model delayed neutrons explicitly, but if your course material mentions them, plan to factor that into your explanation even if the visual output does not show it.
